Related papers: Sampling-Based Global Optimal Control and Estimati…

The recent developments of basis pursuit and compressed sensing seek to extract information from as few samples as possible. In such applications, since the number of samples is restricted, one should deploy the sampling points wisely. We…

In recent years, many estimation problems in robotics have been shown to be solvable to global optimality using their semidefinite relaxations. However, the runtime complexity of off-the-shelf semidefinite programming (SDP) solvers is up to…

Approximating a function with a finite series, e.g., involving polynomials or trigonometric functions, is a critical tool in computing and data analysis. The construction of such approximations via now-standard approaches like least squares…

This paper studies the problem of maximizing the sum of traces of matrix quadratic forms on a product of Stiefel manifolds. This orthogonal trace-sum maximization (OTSM) problem generalizes many interesting problems such as generalized…

This paper studies the polynomial optimization problem whose feasible set is a union of several basic closed semialgebraic sets. We propose a unified hierarchy of Moment-SOS relaxations to solve it globally. Under some assumptions, we prove…

The potential impact of autonomous robots on everyday life is evident in emerging applications such as precision agriculture, search and rescue, and infrastructure inspection. However, such applications necessitate operation in unknown and…

We use the Sum of Squares method to develop new efficient algorithms for learning well-separated mixtures of Gaussians and robust mean estimation, both in high dimensions, that substantially improve upon the statistical guarantees achieved…

This paper presents a practical global optimization algorithm for the K-center clustering problem, which aims to select K samples as the cluster centers to minimize the maximum within-cluster distance. This algorithm is based on a…

The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for…

In this paper, we present a branch and bound algorithm for extracting approximate solutions to Global Polynomial Optimization (GPO) problems with bounded feasible sets. The algorithm is based on a combination of SOS/Moment relaxations and…

Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…

This work is concerned with the proof-complexity of certifying that optimization problems do \emph{not} have good solutions. Specifically we consider bounded-degree "Sum of Squares" (SOS) proofs, a powerful algebraic proof system introduced…

We propose KROM, a kernel-based reduced-order framework for fast solution of nonlinear partial differential equations. KROM formulates PDE solution as a minimum-norm (Gaussian-process) recovery problem in an RKHS, and accelerates the…

This paper introduces the Kernel Neural Operator (KNO), a provably convergent operator-learning architecture that utilizes compositions of deep kernel-based integral operators for function-space approximation of operators (maps from…

This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…

Control system optimization has long been a fundamental challenge in robotics. While recent advancements have led to the development of control algorithms that leverage learning-based approaches, such as SafeOpt, to optimize single feedback…

Bayesian Optimization (BO) is a powerful tool for black-box optimization, but its application to high-dimensional permutation spaces is severely limited by the challenge of defining scalable representations. The current state-of-the-art BO…

We propose kernel distributionally robust optimization (Kernel DRO) using insights from the robust optimization theory and functional analysis. Our method uses reproducing kernel Hilbert spaces (RKHS) to construct a wide range of convex…

Black box optimization (BBO) focuses on optimizing unknown functions in high-dimensional spaces. In many applications, sampling the unknown function is expensive, imposing a tight sample budget. Ongoing work is making progress on reducing…

The minimum sum-of-squares clustering (MSSC), or k-means type clustering, is traditionally considered an unsupervised learning task. In recent years, the use of background knowledge to improve the cluster quality and promote…